The 23-year-old says the Giallorossi cannot afford to lose the services of De Rossi this season due to his importance to the team's dynamic in midfield
De Rossi, who has spent his entire career at the club, has recently hinted he was prepared to remain with the Giallorossi despite interest from Chelsea and Paris Saint-Germain this summer.
And Strootman, who completed a €20 million move from PSV last month, believes the decision will prove beneficial to Roma in the long term.
He told Corriere dello Sport: "I am not worried about the competition for places in the squad. It's better that there is competition. There are 24 players and all of them are very good.
"I am in awe of [Miralem] Pjanic when he starts taking command in midfield, and with De Rossi everything is perfect.
"We understand each other and we know how to play together."
Strootman is not the only addition to the club with coach Rudi Garcia, goalkeeper Morgan De Sanctis and defenders Maicon and Mehdi Benatia, all joining the Giallorossi.